Canonical Basis

linear-algebra

Definition

Canonical Basis

The vectors $e_1,e_2,\dots ,e_n$ form the canonical basis $E=\{e_1,e_2,\dots ,e_n\}$ of the scalar field $F^n$ of a vector space.

$$e_1=\left[\begin{array}{c}1\\ 0\\ ⋮\\ 0\end{array}\right],e_2=\left[\begin{array}{c}0\\ 1\\ ⋮\\ 0\end{array}\right],\dots ,e_n=\left[\begin{array}{c}0\\ 0\\ ⋮\\ 1\end{array}\right]$$